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Lipschitzianity of optimal trajectories for the Bolza optimal control problem

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Abstract

In this paper we investigate Lipschitz continuity of optimal solutions for the Bolza optimal control problem under Tonelli’s type growth condition. Such regularity being a consequence of normal necessary conditions for optimality, we propose new sufficient conditions for normality of state-constrained nonsmooth maximum principles for absolutely continuous optimal trajectories. Furthermore we show that for unconstrained problems any minimizing sequence of controls can be slightly modified to get a new minimizing sequence with nice boundedness properties. Finally, we provide a sufficient condition for Lipschitzianity of optimal trajectories for Bolza optimal control problems with end point constraints and extend a result from (J. Math. Anal. Appl. 143, 301–316, 1989) on Lipschitzianity of minimizers for a classical problem of the calculus of variations with discontinuous Lagrangian to the nonautonomous case.

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Authors and Affiliations

  1. CREA, École Polytechnique, 1 Rue Descartes, 75005, Paris, France

    H. Frankowska & E. M. Marchini

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  1. H. Frankowska
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  2. E. M. Marchini
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Correspondence to H. Frankowska.

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Communicated by L.Ambrosio

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Frankowska, H., Marchini, E.M. Lipschitzianity of optimal trajectories for the Bolza optimal control problem. Calc. Var. 27, 467–492 (2006). https://doi.org/10.1007/s00526-006-0037-x

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  • DOI: https://doi.org/10.1007/s00526-006-0037-x

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